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RE: The Mathematics of Fractional Reserve Banking

in #mathematics9 years ago (edited)

here ill fix it for you so it makes sense sum

Banksum $Lent$ Lent$ResSum $ResliabilitiessumliabilitiesAssets+res-liab
090,000,00090,000,00010,000,00010,000,000100M100M90M+10M-100M=0
1171,000,00081,000,0009,000,00019,000,00090m190M171M+19M-190M=0
2243,900,00072,900,0008,100,00027,100,00081M271M243.9M+27.1M-271M=0
3309,510,00065,610,0007,290,00034,390,00072.9M343.9m309.51M+34.39M-343.9m=0

etc etc... nothing is being created, it all zeroes out... man charts are hard, but you get the point

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What do you mean that nothing is created? Where was that 90% that is loaned out to begin with? I understand that it's a record in a balance sheet. But to claim nothing is created (even ever, as you state by keeping track of assets and liabilities --- you should aggregate reserve with assets, as these are still assets being held on hand by the bank) by using accounting tools is but another way to misguide people who do not understand mathematics.

OK, lets take the money from the Fed only, though i don't think its as special as you do., i agreed to the definition

First of all, its important to understand that this money will not be lent without interest... so in the absence of interest, there is never a money multiplier effect because the money will never get loaned because such a loan is -EV (because the bank breaks even when the loan is paid back, but there is a non-zero chance of them losing money if the loan defaults)... Even though you imply that they profit from it, in your theoretical no interest scenario, all your banks create is .9B in -ev debt.

Lets take two scenarios:

scenrio 1 RR=10%

So we have 100M in the money supply from the fed, Corp A deposits it into bank 0. Lets stick with a closed system. Say theres a 10% reserve. They lend out 90M to corp B, and keep 10M in reserve.

So now corp B has 90M cash monies
Corp A has 100M in deposits at the bank (10% of which is in cash reserve)

So total money supply is 190... it has increased by 90% from the money the fed initially put into the system.

scenario 2 RR=20%

Corp A puts the same 100M into an account at bank 0.
Corp B borrows the same 90M
Bank zero must now bring in an additional 10M from the fed to satisfy reserve requirements.
Our amount of money coming from the fed has increased (its now 110M instead of 100M) but the total money supply has stayed the same (corp a has 100M, corp b has 90M for a total of 190M.

It seems, superficially, that scenario 1 presents a greater increase beyond what is supplied to the system from the fed, since scenario B requires 10M more input to get the same output.

And, provided COrp A never wants to use any of their their money, this works. But now, lets say corp A wants to use 20M of their money.

scenario 1, 6 months later

Corp A makes a 20M wd.

In scenario 1, bank 0 has 10M in reserve. They must pay 20M to corp A, and still maintain a 8M reserve. So they must bring in an additional 18M to pay corp A and still have sufficient resercves. So in addition to the 100M brought in initially, there is now 18M additional money from the fed brought into the system.

Now corp A has 80M on deposit
Corp A has 20M in cash
corp B has 90M in cash

Since no new money was lent, the money supply is still 190, coming from a total of 118M brought in from the fed. (100 at the beginning and 18 now)

Scenario 2, 6 months later

COrp A decides to withdrawal the same 20M
Bank 0 has 20M in reserve that it uses to pay corp A, then borrows 16M to satisfy reserve requirements.

In total, 16M (now) plus 110M (at the beginning) has been brought in.

So thats 126M from the fed that turns into 190M.

scenario 1, 1 year later

Now corp A wants to take out its remaining 80M . The bank has 8M in reserve, and has to borrow the rest (72M) from the fed.

Now corp A has 100m cash
corp B has 90m in cash

and a total 190M (118+72) has come in from the fed, and the money supply is 190

scenario 2, 1 year later

COrp a WD's their remaining 80M. 16M is in the bank as reserve, and the bank has to borrow 64M.

TOtal money brought in from the fed 190M total money supply 190M

So the difference in the money coming from the fed and money supply in the two different RR scenarios converges as corp A actually uses the money it has in the bank.

So, yes, when banks borrow from the fed, then loan and reloan the money, a lower reserve rate does increase the growth of the money supply beyond what was initially borrowed. BUT, it only does so for money thats sitting in the bank doing doing nothing at all. That money thats just an account balance makes no differnce anyway, though. Its not as though the bank profits from having it sit there on the books.

Its kind like a tree falling in the wilderness. If money is sitting in the bank and mouldering, is it really part of the money supply. Are satoshis coins part of the BTC money supply? THey exist, but they don't get spent ever.

If you go back to the second paragraph above, i explained that banks dont lend money for free. A corollary of this is that companies don't borrow money for nothing. Sooner or later, these companies are going to want to use their money on deposit, and that means the bank where theyre holding their deposits is going have to go to the fed and borrow that money back... because this statement you made was absolutely correct....

the effect of the reserve rate is how much of that money is going to have to come from the fed ad initio, when they make the first loan and how much is going to have to be borrowed later, to satisfy reserve requirements. As company A decides to withdrawal and use its money on deposit.

As you stated earlier:

In other words, the effective mathematical difference is zilch, if a loan is made from deposits (as in my example) or from bankers making rational banking decisions as to creating loans and then loaning from a Central Bank to meet reserve requirements

And you were completely right. all the RR rate does is determine when a bank is going to bring money in from the fed. ANd it doesnt really matter when.

The only time the RR has a real impact on the growth of the money supply is in the highly theoretical situation where business pay to borrow money, then let it sit in the bank. Which pretty much never happens.

Thank you! This is what I wanted to see.

However, in your scenarios where you show that there is no money multiplication, this assumes that no money is kept in the bank at some point in time and that all capital is kept in the form of cash.

But, that's the whole point of how money multiplication effect works is when any amount is kept in a bank.

That is to say, the total amount loaned out from a central bank will always be less than or equal to the total amount of money in circulation.

As such, the only way for money multiplication to not occur is for everyone to hold onto their cash and not deposit in the bank.

So, yes, when banks borrow from the fed, then loan and reloan the money, a lower reserve rate does increase the growth of the money supply beyond what was initially borrowed. BUT, it only does so for money thats sitting in the bank doing doing nothing at all. That money thats just an account balance makes no differnce anyway, though. Its not as though the bank profits from having it sit there on the books. (emphasis mine)

I thought that was the math I was saying the entire time ...

I realize i used a cash withdrawal as an example, but it doesnt necessarily have to be a cash withdrawal (and in fact it would be almost as rare for it to be a cash withdrawal as it would be for it to be held on deposit) What it would typically be for borrowed money is a capital expenditure.

ANd yeah, it might go right into another bank if this was the case (in fact its very likely that it would, but thats not going to change the amount of money.)

So lets take scenario 1 again, but instead of making cash withdrawals, company A buys a building from company C for $100. Company C banks at bank 1.

So company A wires the money from his bank(bank 0) to company C's bank (bank 1).

Bank 0 is still going to pull the extra money in from the fed to pay bank 1 (actually thats not 100% what would happen the bank 1 would just lend the money to bank 0 overnight, then have the fed send it the next day but its effectively the same thing)

Sure, I understand that cash has no real value, only in that others perceive that it has value. Much like anything else in the world.

Well, yeah all value is perceived value. But my point was that a dollar bill doesn't even have perceived value beyond the fact that you can put it in a fed reserve operated bank and get $1 in balance credit for it. Its Its bank balances that have percieved value. FRNs are just tokens, like coat check tickets. When you go to buy groceries, the checker doesnt take cash because he or the store owner percieves value in a dollar bill. They take cash because they believe they'll be able to deposit it in the bank. If i tried to pay with one of my two beautiful McKinley 500s, which i never would because theyre worth about $1000 ea as collectors items, they wouldn't accept them. Because they can't be deposited in the bank. Because at some point in the 1970s, the fed said theyre not accepting them anymore.

So when you say that, for example, the Fed doesnt have enough FRNs to cover the totality of deposits because of money multiplication... if thats true (and it might well be) its irrelevant. Because more can simply be printed , should they be required.

OK, going back through some of the things i saw posted in the thread... you get that cash.. like actual physical green paper currency, doesn't have any real value, right.... like when you say 900M funny money in the OP, its not funny money because we don't have actual physical bank notes to back it up, is it?

Yeah... i get that the reserve is part of assets... i seperated it out to show where the money comes from.

As to your question, "where was the 90% tht was loaned out" It was on deposit. then it was loaned out. I dont really get what youre not seeing.

private school 5 or public school 5? couldnt help myself

Ill be honest with you, i really don't know how i can explain anything to you. If you believe that balance sheets are a scam created by the international banking conspiracy and basic accounting is just a fairy tale to exploit the disenfranchised masses, i don't even know where i could start.

Its like if i was trying to explain electricity to someone from the 5th century who thought that any explanation for natural phenonema that didnt involve evil spirits was a ploy of the devil... there has to be at least some kind of common ground.

Im not trying to talk down... i just don't see how someone can be convinced if hes willing to dismiss anything that doesnt agree with his preconcieved notions as some kind of sinister conspiracy.

I could put a bunch of big numbers in a chart and jump up and down yelling conspiracy! conspiracy! that seems like the kind of argument that might win over a five year old.

I only just now saw your comment about private or public school 5.

No. Explain the concepts to me as someone with an advanced degree in pure mathematics but is not familiar with the terms of your discipline and is trying to interact in an amicable manner.

I would really appreciate how you wave your hands at the explanation that money multiplication does not occur when purely business decisions are being made to determine if a loan is made and then borrowing from a central bank as necessary to meet reserve requirements, assuming this is done under a system with reserve requirements.

If the underlying definition of money multiplication is one where there is any increase in the monetary supply beyond the original amount borrowed from a central bank AND IF there exists a reserve requirement, then it makes no difference if the loan that is made by a bank is covered by reserve requirements before or after that loan is made.

ALso, as to the increase in money supply based on lending being based on a math phenonemon. It is, just not the one you think. Yes, absolutely, the money supply increases because banks lend out money. But that would be true even with a full 100% reserve. Lending creates money.

With 100% reserve, one cannot apply infinite geometric series and sequences ...

But, assuming 100% reserve requirement, I agree that money is created via lending only, and, as you've stated before, this is nothing more than an accounting mechanism, debits and credits on the books, which all nicely sum to 0.

Take fractional reserve out of banking, and force banks to lend entirely on capital... do you know what you get? We do have a system like that in the US. 10 Steem to the first one that can figure out what it is.

I'll match this as well to anyone who can adequately answer that question.

Regardless, money multiplication comes from the sheer fact that banks can lend money.

How this loaning and determination is done, based on some formula designed under particular models that assumes various risk aspects and, statistically, guarantees a positive expected value for the bank, is completely separate from how money is created.

Through the process of lending.

OK. Sure. I can agree that it's not via deposits.

I still do not see how money multiplication doesn't occur when banks can lend whatever they need to and then borrow the appropriate amount from the central bank to meet reserve requirements.

(Apologies for the post edits and deletions ... multiple browsers, and didn't realize I responded twice -- responses have been concatenated)

And explain to me like I am 5 how there is no money multiplier effect when the total amount that is loaned out and in circulation is more than the total amount that was originally borrowed from the Federal Reserve?

I don't really get what you're not seeing about how that isn't money multiplication ...

With 100% reserve, one cannot apply infinite geometric series and sequences

Not in a closed system, no. But the economy isnt a closed system. Lets say im SigmaBank, instead of Sigmajin. And i run the first national bank of steemsville. In steemsville, there is a 100% reserve, so i can't lend money on my deposit account balances. I have company B in my loan office and they want a 100000 steem loan. I want to write the loan. Im fucked, right? 100% reserve. My deposits are spoken for.

FOrtunately, I know complexring. Complex is rich as all hell and he has 300K steem on deposit. He has millions of dollars in steem that he cant possibly use all of. So i say to complex, "why don't you take 100K steem out of your bank account, and give it to me. Ill write you an IOU, lend it out, and well split the interest."

You know im good for it because im a fucking bank... its not like im going to run off. If you didnt trust me, you wouldnt have 300K steem on deposit in the first place.

So you give 100K and i loan it to company B, then i write you an IOU for 100K plusinterest and pay you back as they pay me. So you get the principle payments, plus half the interest payments, and I get half the interest. Yeah, you personally might not be down, but in the wider economic world, there are absolutely a huge number of rich people that are down.

Now lets say company B isnt using the whole 100K steem they borrowed, they can make the same deal with me that you did so i can write a loan to company C. The only difference between this scenario and the one you present is that the banks liabilities are now in the form of IOUs, not in the form of deposit liabilities.

But it gets even better... because you know that IOU i wrote you, you can actually sell that IOU to someone else. Its called a debt security... and as long as sigmabank hasnt fucked up its credit, youll be able to sell it for probably nearly full face value. So lets say the 100K steem was for a house, and the 30 year mortgage repayment was slated to be around 200K steem.... your IOU is for 100% of principle, and 50% of interest, or 150K... youll be able to usually get between 110 and 125K on it. Which, if i can find another borrower, you can just lend back to me.

Like your scenario, it depends on the idea that a company would be willing to borrow a lot of money, then leave most of it in the bank, so that the bank could loan it out again..... the only difference is now they are explicitly loaning it to the bank, rather than simply leaving it on deposit.

So ... how does this all relate to loaning money to a bank and the bank loaning it out to others with respect to money multiplication, as per the definition that it is any increased supply beyond the original amount borrowed from the central bank.

also note that the primary difference here is that you would consider your Steem as already part of the money supply, even though you arent actively using it. Whereas you consider central bank money as coming in from the outside.

But all youre showing at the end of the day is that if enough people are willing to borrow money, then leave borrowed money sitting in the bank, that the bank can make a killing lending out the same borrowed money over and over. The accounting is different with a 100% reserve, but it depends on the same thing... multiple companies being willing to let the bank hold money that they borrowed.

Further side note... this is why when the fed wants to decrease money supply, they don't hike up the reserve rate, they hike up fed interest rates... that way its more expensive for banks to borrow money, so they have to be more selective about who they lend it to (or they have to charge more interest) so the demand for loans decreases.

I can't reply to sigmajin because of nesting limits, but I don't think the Federal Reserve has the interest rate set next to nothing right now because they want to. Their quantitative easing plan was to make lending money cheaply to avoid a prolonged recession (or Great Depression 2.0) but now they can't raise rates again because the US government will not be able to pay up. Think of how much interest 20 trillion dollars will rack up with a higher rate.

@theabsolute yeah, they definitely want to... I dont think its wise, but its definitely policy. They spent most of the first half of this year banging the NIRP gong. Its dead now, but if trump wins, i doubt itll stay dead (and tbh i dont think hillary would necessarily be against it either)... right now, everyone is terrified of a recession... like if politicians thought it would help, or even thought that the electorate thought it would help, i could easily imagine them sacrificing people like in the shirley jackson short story. .

The ECB and japans central bank both have NIRP right now.

Excellent post once again.